Anisotropic damage–plasticity model for concrete

• Published in: International journal of plasticity 2008-10, Vol.24 (10), p.1946-1965
• Main Authors: Voyiadjis, George Z., Taqieddin, Ziad N., Kattan, Peter I.
• Format: Article
• Language: English
• Subjects: Anisotropic continuum damage mechanics; Anisotropy; Concrete plasticity; Concretes; Criteria; Damage; Damage–elasto-plastic tangent operator; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Mathematical analysis; Mathematical models; Physics; Plasticity; Solid mechanics; Strain energy equivalence; Structural and continuum mechanics; Tensors; Thermodynamics
• ISSN: 0749-6419; 1879-2154
• DOI: 10.1016/j.ijplas.2008.04.002

A material model for concrete is proposed here within the framework of a thermodynamically consistent elasto-plasticity–damage theory. Two anisotropic damage tensors and two damage criteria are adopted to describe the distinctive degradation of the mechanical properties of concrete under tensile and compressive loadings. The total stress tensor is decomposed into tensile and compressive components in order to accommodate the need for the above mentioned damage tensors. The plasticity yield criterion presented in this work accounts for the spectral decomposition of the stress tensor and allows multiple hardening rules to be used. This plastic yield criterion is used simultaneously with the damage criteria to simulate the physical behavior of concrete. Non-associative flow rule for the plastic strains is used to account for the dilatancy of concrete as a frictional material. The thermodynamic Helmholtz free energy concept is used to consistently derive dissipation potentials for damage and plasticity and to allow evolution laws for different hardening parameters. The evolution of the two damage tensors is accounted for through the use of fracture-energy-based continuum damage mechanics. An expression is derived for the damage–elasto-plastic tangent operator. The theoretical framework of the model is described here while the implementation of this model will be discussed in a subsequent paper.